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katrin2010 [14]
2 years ago
15

A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only

wants a 2% margin of error at a 97.5% confidence level, what size of sample is needed?Give your answer in whole people.
Mathematics
1 answer:
makvit [3.9K]2 years ago
7 0

Answer:

The sample size is  n = 3139    

Step-by-step explanation:

From the question we are told that

   The margin of error is  E = 0.02

From the question we are told the confidence level is  97.5% , hence the level of significance is    

      \alpha = (100 - 97.5% ) \%

=>   \alpha = 0.025

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } = 2.241

Generally we will assume the sample proportion to be \^ p = 0.5

Generally the sample size is mathematically represented as  

    n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )

=>  n = [\frac{2.241}{0.02} ]^2 *0.5 (1 - 0.5 )

=>  n = 3139    

   

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Ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

Step-by-step explanation:

Let the number of red fish and blue fish in the large tank are x and y respectively.

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Since in each tank ratio of the red fish to blue fish is 333 : 444

That means x : y = 333 : 444

Or \frac{x}{y}=\frac{333}{444}

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Similarly x' : y' = 333 : 444

⇒ \frac{x'}{y'}=\frac{333}{444}

⇒ \frac{x'}{y'}=\frac{3}{4}

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Ratio of the fish in large tank to the fish in small tank is 464646 : 555

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Now we replace the values of x and y' from equation (1) and equation (2)

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\frac{4}{3}\times \frac{x}{y'}=\frac{464646}{555}

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\frac{x}{y'}=\frac{232323}{370}

\frac{y'}{x}=\frac{370}{232323}

\frac{y'}{x}=\frac{10}{6279}

Therefore, ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

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